giving up vs forgoing

giving up and forgoing both are nouns.

Word	Noun	Adjective	Verb	Adverb
giving up	Yes	No	No	No
forgoing	Yes	No	No	No

As nouns, forgoing is a hypernym of giving up; that is, forgoing is a word with a broader meaning than giving up:

giving up: the act of forsaking
forgoing: the act of renouncing; sacrificing or giving up or surrendering (a possession or right or title or privilege etc.)

Other hypernyms of giving up include forswearing, renunciation.

giving up (noun)	forgoing (noun)
the act of forsaking	the act of renouncing; sacrificing or giving up or surrendering (a possession or right or title or privilege etc.)
a verbal act of admitting defeat